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Wire the Lean 4 backend into the proof agent - #8

Draft
dingf3ng wants to merge 4 commits into
NUS-Program-Verification:mainfrom
dingf3ng:contrib/lean-wired
Draft

Wire the Lean 4 backend into the proof agent#8
dingf3ng wants to merge 4 commits into
NUS-Program-Verification:mainfrom
dingf3ng:contrib/lean-wired

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@dingf3ng

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Summary

  • run the proof agent end to end through ProverBackend and the Lean 4 adapter
  • remove the legacy CoqInterface runtime and test path
  • expose only Lean 4 in this independently testable stack tip
  • add controller, CLI, rendering, cleanup, and real prover workflow coverage

Stack dependency

Draft; depends on #5. The narrow wiring-only diff is available in the fork at dingf3ng#6. Until the lower PRs merge, GitHub shows their commits here as well.

Verification

  • 119 deterministic tests passed; the real Lean agent workflow and certificate replay passed in 25.32s.
  • No Python reference to CoqInterface or either unrelated adapter remains.

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